Average Error: 0.2 → 0.2
Time: 6.7s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r2148 = x;
        double r2149 = cosh(r2148);
        double r2150 = y;
        double r2151 = sin(r2150);
        double r2152 = r2151 / r2150;
        double r2153 = r2149 * r2152;
        return r2153;
}
↓
double f(double x, double y) {
        double r2154 = x;
        double r2155 = cosh(r2154);
        double r2156 = y;
        double r2157 = sin(r2156);
        double r2158 = r2157 / r2156;
        double r2159 = r2155 * r2158;
        return r2159;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

    \[\cosh x \cdot \frac{\sin y}{y}\]

  2. Final simplification0.2

    \[\leadsto \cosh x \cdot \frac{\sin y}{y}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))